(a)
To construct:A choice table for interest tables from 0% to 100% assuming doing nothing is allowed.
(a)
Answer to Problem 22P
From table below, from 0% to 4.7%, Alternative C should be preferred. Between 4.7% to 6.9%; Alternative B should be preferred. Alternative A should be preferred for interest rate between 6.9% to 8.2%.
Explanation of Solution
NPV of Alternative B
NPV of Alternative C
Choice table for interest from 0% to 100%
Interest rate | (A/P,i,2) | (A/P,i,4) | (P/A,i,8) | A | B | C |
0% | 0.500 | 0.250 | 8.000 | 400 | 600 | 850 |
1% | 0.508 | 0.256 | 7.652 | 337 | 502 | 693 |
2% | 0.515 | 0.263 | 7.325 | 278 | 411 | 546 |
3% | 0.523 | 0.269 | 7.020 | 224 | 326 | 409 |
4% | 0.530 | 0.275 | 6.733 | 174 | 248 | 280 |
5% | 0.538 | 0.282 | 6.463 | 128 | 174 | 158 |
6% | 0.545 | 0.289 | 6.210 | 85 | 106 | 44 |
7% | 0.553 | 0.295 | 5.971 | 45 | 43 | (63) |
8% | 0.561 | 0.302 | 5.747 | 8 | (17) | (164) |
9% | 0.568 | 0.309 | 5.535 | (26) | (72) | (259) |
10% | 0.576 | 0.315 | 5.335 | (58) | (124) | (349) |
11% | 0.584 | 0.322 | 5.146 | (88) | (172) | (434) |
12% | 0.592 | 0.329 | 4.968 | (116) | (218) | (515) |
13% | 0.599 | 0.336 | 4.799 | (142) | (261) | (591) |
14% | 0.607 | 0.343 | 4.639 | (166) | (301) | (663) |
15% | 0.615 | 0.350 | 4.487 | (189) | (338) | (731) |
16% | 0.623 | 0.357 | 4.344 | (210) | (374) | (795) |
17% | 0.631 | 0.365 | 4.207 | (230) | (407) | (857) |
18% | 0.639 | 0.372 | 4.078 | (249) | (439) | (915) |
19% | 0.647 | 0.379 | 3.954 | (266) | (469) | (971) |
20% | 0.655 | 0.386 | 3.837 | (283) | (497) | (1,023) |
21% | 0.662 | 0.394 | 3.726 | (298) | (523) | (1,073) |
22% | 0.670 | 0.401 | 3.619 | (313) | (548) | (1,121) |
23% | 0.678 | 0.408 | 3.518 | (326) | (572) | (1,167) |
24% | 0.686 | 0.416 | 3.421 | (339) | (595) | (1,210) |
25% | 0.694 | 0.423 | 3.329 | (351) | (616) | (1,252) |
26% | 0.702 | 0.431 | 3.241 | (363) | (637) | (1,292) |
27% | 0.711 | 0.439 | 3.156 | (374) | (656) | (1,330) |
28% | 0.719 | 0.446 | 3.076 | (384) | (675) | (1,366) |
29% | 0.727 | 0.454 | 2.999 | (394) | (692) | (1,401) |
30% | 0.735 | 0.462 | 2.925 | (403) | (709) | (1,434) |
31% | 0.743 | 0.469 | 2.854 | (412) | (725) | (1,466) |
32% | 0.751 | 0.477 | 2.786 | (420) | (740) | (1,496) |
33% | 0.759 | 0.485 | 2.721 | (428) | (755) | (1,526) |
34% | 0.767 | 0.493 | 2.658 | (436) | (769) | (1,554) |
35% | 0.776 | 0.501 | 2.598 | (443) | (782) | (1,581) |
36% | 0.784 | 0.509 | 2.540 | (450) | (795) | (1,607) |
37% | 0.792 | 0.517 | 2.485 | (456) | (808) | (1,632) |
38% | 0.800 | 0.525 | 2.432 | (462) | (819) | (1,656) |
39% | 0.808 | 0.533 | 2.380 | (468) | (831) | (1,679) |
40% | 0.817 | 0.541 | 2.331 | (474) | (842) | (1,701) |
41% | 0.825 | 0.549 | 2.283 | (479) | (852) | (1,723) |
42% | 0.833 | 0.557 | 2.237 | (484) | (862) | (1,743) |
43% | 0.842 | 0.565 | 2.193 | (489) | (872) | (1,763) |
44% | 0.850 | 0.573 | 2.150 | (494) | (881) | (1,783) |
45% | 0.858 | 0.582 | 2.109 | (499) | (891) | (1,801) |
46% | 0.867 | 0.590 | 2.069 | (503) | (899) | (1,819) |
47% | 0.875 | 0.598 | 2.030 | (507) | (908) | (1,836) |
48% | 0.883 | 0.606 | 1.993 | (511) | (916) | (1,853) |
49% | 0.892 | 0.615 | 1.957 | (515) | (924) | (1,869) |
50% | 0.900 | 0.623 | 1.922 | (519) | (931) | (1,885) |
51% | 0.908 | 0.631 | 1.888 | (523) | (939) | (1,900) |
52% | 0.917 | 0.640 | 1.856 | (526) | (946) | (1,915) |
53% | 0.925 | 0.648 | 1.824 | (529) | (953) | (1,929) |
54% | 0.934 | 0.657 | 1.793 | (533) | (960) | (1,943) |
55% | 0.942 | 0.665 | 1.764 | (536) | (966) | (1,956) |
56% | 0.951 | 0.674 | 1.735 | (539) | (973) | (1,969) |
57% | 0.959 | 0.682 | 1.707 | (542) | (979) | (1,982) |
58% | 0.968 | 0.691 | 1.680 | (544) | (985) | (1,994) |
59% | 0.976 | 0.699 | 1.653 | (547) | (991) | (2,006) |
60% | 0.985 | 0.708 | 1.628 | (550) | (996) | (2,017) |
61% | 0.993 | 0.717 | 1.603 | (552) | (1,002) | (2,029) |
62% | 1.002 | 0.725 | 1.579 | (555) | (1,007) | (2,039) |
63% | 1.010 | 0.734 | 1.555 | (557) | (1,013) | (2,050) |
64% | 1.019 | 0.743 | 1.533 | (559) | (1,018) | (2,060) |
65% | 1.027 | 0.751 | 1.510 | (562) | (1,023) | (2,070) |
66% | 1.036 | 0.760 | 1.489 | (564) | (1,028) | (2,080) |
67% | 1.045 | 0.769 | 1.468 | (566) | (1,032) | (2,089) |
68% | 1.053 | 0.778 | 1.447 | (568) | (1,037) | (2,099) |
69% | 1.062 | 0.786 | 1.427 | (570) | (1,042) | (2,108) |
70% | 1.070 | 0.795 | 1.408 | (572) | (1,046) | (2,116) |
71% | 1.079 | 0.804 | 1.389 | (574) | (1,050) | (2,125) |
72% | 1.088 | 0.813 | 1.371 | (576) | (1,055) | (2,133) |
73% | 1.096 | 0.822 | 1.353 | (578) | (1,059) | (2,141) |
74% | 1.105 | 0.831 | 1.335 | (579) | (1,063) | (2,149) |
75% | 1.114 | 0.840 | 1.318 | (581) | (1,067) | (2,157) |
76% | 1.122 | 0.848 | 1.301 | (583) | (1,071) | (2,164) |
77% | 1.131 | 0.857 | 1.285 | (585) | (1,074) | (2,172) |
78% | 1.140 | 0.866 | 1.269 | (586) | (1,078) | (2,179) |
79% | 1.148 | 0.875 | 1.254 | (588) | (1,082) | (2,186) |
80% | 1.157 | 0.884 | 1.239 | (589) | (1,085) | (2,193) |
81% | 1.166 | 0.893 | 1.224 | (591) | (1,089) | (2,199) |
82% | 1.175 | 0.902 | 1.209 | (592) | (1,092) | (2,206) |
83% | 1.183 | 0.911 | 1.195 | (594) | (1,096) | (2,212) |
84% | 1.192 | 0.920 | 1.181 | (595) | (1,099) | (2,218) |
85% | 1.201 | 0.929 | 1.168 | (596) | (1,103) | (2,224) |
86% | 1.210 | 0.938 | 1.155 | (598) | (1,106) | (2,230) |
87% | 1.218 | 0.947 | 1.142 | (599) | (1,109) | (2,236) |
88% | 1.227 | 0.957 | 1.129 | (600) | (1,112) | (2,242) |
89% | 1.236 | 0.966 | 1.117 | (602) | (1,115) | (2,247) |
90% | 1.245 | 0.975 | 1.105 | (603) | (1,118) | (2,253) |
91% | 1.254 | 0.984 | 1.093 | (604) | (1,121) | (2,258) |
92% | 1.262 | 0.993 | 1.081 | (605) | (1,124) | (2,264) |
93% | 1.271 | 1.002 | 1.070 | (607) | (1,127) | (2,269) |
94% | 1.280 | 1.011 | 1.059 | (608) | (1,130) | (2,274) |
95% | 1.289 | 1.021 | 1.048 | (609) | (1,132) | (2,279) |
96% | 1.298 | 1.030 | 1.037 | (610) | (1,135) | (2,283) |
97% | 1.307 | 1.039 | 1.026 | (611) | (1,138) | (2,288) |
98% | 1.316 | 1.048 | 1.016 | (612) | (1,140) | (2,293) |
99% | 1.324 | 1.057 | 1.006 | (613) | (1,143) | (2,297) |
100% | 1.333 | 1.067 | 0.996 | (614) | (1,146) | (2,302) |
(b)
To construct:A choice table for interest tables from 0% to 100% assuming A, B o r C must be chosen.
(b)
Answer to Problem 22P
From table below, from 0% to 4.7%, Alternative C should be preferred. Between 4.7% to 6.9%; Alternative B should be preferred. Beyond that Alternative A should be preferred for interest rate between 6.9% to 100%.
Explanation of Solution
NPV of Alternative A
NPV of Alternative B
NPV of Alternative C
Choice table for interest from 0% to 100%
Interest rate | (A/P,i,2) | (A/P,i,4) | (P/A,i,8) | A | B | C |
0% | 0.500 | 0.250 | 8.000 | 400 | 600 | 850 |
1% | 0.508 | 0.256 | 7.652 | 337 | 502 | 693 |
2% | 0.515 | 0.263 | 7.325 | 278 | 411 | 546 |
3% | 0.523 | 0.269 | 7.020 | 224 | 326 | 409 |
4% | 0.530 | 0.275 | 6.733 | 174 | 248 | 280 |
5% | 0.538 | 0.282 | 6.463 | 128 | 174 | 158 |
6% | 0.545 | 0.289 | 6.210 | 85 | 106 | 44 |
7% | 0.553 | 0.295 | 5.971 | 45 | 43 | (63) |
8% | 0.561 | 0.302 | 5.747 | 8 | (17) | (164) |
9% | 0.568 | 0.309 | 5.535 | (26) | (72) | (259) |
10% | 0.576 | 0.315 | 5.335 | (58) | (124) | (349) |
11% | 0.584 | 0.322 | 5.146 | (88) | (172) | (434) |
12% | 0.592 | 0.329 | 4.968 | (116) | (218) | (515) |
13% | 0.599 | 0.336 | 4.799 | (142) | (261) | (591) |
14% | 0.607 | 0.343 | 4.639 | (166) | (301) | (663) |
15% | 0.615 | 0.350 | 4.487 | (189) | (338) | (731) |
16% | 0.623 | 0.357 | 4.344 | (210) | (374) | (795) |
17% | 0.631 | 0.365 | 4.207 | (230) | (407) | (857) |
18% | 0.639 | 0.372 | 4.078 | (249) | (439) | (915) |
19% | 0.647 | 0.379 | 3.954 | (266) | (469) | (971) |
20% | 0.655 | 0.386 | 3.837 | (283) | (497) | (1,023) |
21% | 0.662 | 0.394 | 3.726 | (298) | (523) | (1,073) |
22% | 0.670 | 0.401 | 3.619 | (313) | (548) | (1,121) |
23% | 0.678 | 0.408 | 3.518 | (326) | (572) | (1,167) |
24% | 0.686 | 0.416 | 3.421 | (339) | (595) | (1,210) |
25% | 0.694 | 0.423 | 3.329 | (351) | (616) | (1,252) |
26% | 0.702 | 0.431 | 3.241 | (363) | (637) | (1,292) |
27% | 0.711 | 0.439 | 3.156 | (374) | (656) | (1,330) |
28% | 0.719 | 0.446 | 3.076 | (384) | (675) | (1,366) |
29% | 0.727 | 0.454 | 2.999 | (394) | (692) | (1,401) |
30% | 0.735 | 0.462 | 2.925 | (403) | (709) | (1,434) |
31% | 0.743 | 0.469 | 2.854 | (412) | (725) | (1,466) |
32% | 0.751 | 0.477 | 2.786 | (420) | (740) | (1,496) |
33% | 0.759 | 0.485 | 2.721 | (428) | (755) | (1,526) |
34% | 0.767 | 0.493 | 2.658 | (436) | (769) | (1,554) |
35% | 0.776 | 0.501 | 2.598 | (443) | (782) | (1,581) |
36% | 0.784 | 0.509 | 2.540 | (450) | (795) | (1,607) |
37% | 0.792 | 0.517 | 2.485 | (456) | (808) | (1,632) |
38% | 0.800 | 0.525 | 2.432 | (462) | (819) | (1,656) |
39% | 0.808 | 0.533 | 2.380 | (468) | (831) | (1,679) |
40% | 0.817 | 0.541 | 2.331 | (474) | (842) | (1,701) |
41% | 0.825 | 0.549 | 2.283 | (479) | (852) | (1,723) |
42% | 0.833 | 0.557 | 2.237 | (484) | (862) | (1,743) |
43% | 0.842 | 0.565 | 2.193 | (489) | (872) | (1,763) |
44% | 0.850 | 0.573 | 2.150 | (494) | (881) | (1,783) |
45% | 0.858 | 0.582 | 2.109 | (499) | (891) | (1,801) |
46% | 0.867 | 0.590 | 2.069 | (503) | (899) | (1,819) |
47% | 0.875 | 0.598 | 2.030 | (507) | (908) | (1,836) |
48% | 0.883 | 0.606 | 1.993 | (511) | (916) | (1,853) |
49% | 0.892 | 0.615 | 1.957 | (515) | (924) | (1,869) |
50% | 0.900 | 0.623 | 1.922 | (519) | (931) | (1,885) |
51% | 0.908 | 0.631 | 1.888 | (523) | (939) | (1,900) |
52% | 0.917 | 0.640 | 1.856 | (526) | (946) | (1,915) |
53% | 0.925 | 0.648 | 1.824 | (529) | (953) | (1,929) |
54% | 0.934 | 0.657 | 1.793 | (533) | (960) | (1,943) |
55% | 0.942 | 0.665 | 1.764 | (536) | (966) | (1,956) |
56% | 0.951 | 0.674 | 1.735 | (539) | (973) | (1,969) |
57% | 0.959 | 0.682 | 1.707 | (542) | (979) | (1,982) |
58% | 0.968 | 0.691 | 1.680 | (544) | (985) | (1,994) |
59% | 0.976 | 0.699 | 1.653 | (547) | (991) | (2,006) |
60% | 0.985 | 0.708 | 1.628 | (550) | (996) | (2,017) |
61% | 0.993 | 0.717 | 1.603 | (552) | (1,002) | (2,029) |
62% | 1.002 | 0.725 | 1.579 | (555) | (1,007) | (2,039) |
63% | 1.010 | 0.734 | 1.555 | (557) | (1,013) | (2,050) |
64% | 1.019 | 0.743 | 1.533 | (559) | (1,018) | (2,060) |
65% | 1.027 | 0.751 | 1.510 | (562) | (1,023) | (2,070) |
66% | 1.036 | 0.760 | 1.489 | (564) | (1,028) | (2,080) |
67% | 1.045 | 0.769 | 1.468 | (566) | (1,032) | (2,089) |
68% | 1.053 | 0.778 | 1.447 | (568) | (1,037) | (2,099) |
69% | 1.062 | 0.786 | 1.427 | (570) | (1,042) | (2,108) |
70% | 1.070 | 0.795 | 1.408 | (572) | (1,046) | (2,116) |
71% | 1.079 | 0.804 | 1.389 | (574) | (1,050) | (2,125) |
72% | 1.088 | 0.813 | 1.371 | (576) | (1,055) | (2,133) |
73% | 1.096 | 0.822 | 1.353 | (578) | (1,059) | (2,141) |
74% | 1.105 | 0.831 | 1.335 | (579) | (1,063) | (2,149) |
75% | 1.114 | 0.840 | 1.318 | (581) | (1,067) | (2,157) |
76% | 1.122 | 0.848 | 1.301 | (583) | (1,071) | (2,164) |
77% | 1.131 | 0.857 | 1.285 | (585) | (1,074) | (2,172) |
78% | 1.140 | 0.866 | 1.269 | (586) | (1,078) | (2,179) |
79% | 1.148 | 0.875 | 1.254 | (588) | (1,082) | (2,186) |
80% | 1.157 | 0.884 | 1.239 | (589) | (1,085) | (2,193) |
81% | 1.166 | 0.893 | 1.224 | (591) | (1,089) | (2,199) |
82% | 1.175 | 0.902 | 1.209 | (592) | (1,092) | (2,206) |
83% | 1.183 | 0.911 | 1.195 | (594) | (1,096) | (2,212) |
84% | 1.192 | 0.920 | 1.181 | (595) | (1,099) | (2,218) |
85% | 1.201 | 0.929 | 1.168 | (596) | (1,103) | (2,224) |
86% | 1.210 | 0.938 | 1.155 | (598) | (1,106) | (2,230) |
87% | 1.218 | 0.947 | 1.142 | (599) | (1,109) | (2,236) |
88% | 1.227 | 0.957 | 1.129 | (600) | (1,112) | (2,242) |
89% | 1.236 | 0.966 | 1.117 | (602) | (1,115) | (2,247) |
90% | 1.245 | 0.975 | 1.105 | (603) | (1,118) | (2,253) |
91% | 1.254 | 0.984 | 1.093 | (604) | (1,121) | (2,258) |
92% | 1.262 | 0.993 | 1.081 | (605) | (1,124) | (2,264) |
93% | 1.271 | 1.002 | 1.070 | (607) | (1,127) | (2,269) |
94% | 1.280 | 1.011 | 1.059 | (608) | (1,130) | (2,274) |
95% | 1.289 | 1.021 | 1.048 | (609) | (1,132) | (2,279) |
96% | 1.298 | 1.030 | 1.037 | (610) | (1,135) | (2,283) |
97% | 1.307 | 1.039 | 1.026 | (611) | (1,138) | (2,288) |
98% | 1.316 | 1.048 | 1.016 | (612) | (1,140) | (2,293) |
99% | 1.324 | 1.057 | 1.006 | (613) | (1,143) | (2,297) |
100% | 1.333 | 1.067 | 0.996 | (614) | (1,146) | (2,302) |
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Chapter 8 Solutions
ENGR.ECONOMIC ANALYSIS
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